let p, s, q be Element of HP-WFF ; :: thesis: ((p '&' s) => q) => ((p '&' s) => (q '&' s)) in HP_TAUT
set P = p '&' s;
A1: (p '&' s) => s in HP_TAUT by Def10;
((p '&' s) => q) => (((p '&' s) => s) => ((p '&' s) => (q '&' s))) in HP_TAUT by Th35;
hence ((p '&' s) => q) => ((p '&' s) => (q '&' s)) in HP_TAUT by A1, Th29; :: thesis: verum